Spatiotemporal kinetics of the SRP pathway in live E. coli cells

Significance Most of the proteins in all organisms are synthesized in the cell cytosol. However, a substantial fraction of these proteins have their function somewhere else, and cells therefore need protein targeting systems to relocate proteins during or after their synthesis. The signal recognition particle (SRP) is a universal player in protein targeting, but biochemical studies of its dynamics have been problematic since the geometric constraints inside living cells are hard to mimic in the test tube. Using single-molecule tracking, we have followed how SRP targets proteins to the membrane-bound translocation complexes, directly in living bacterial cells. Our kinetic measurements of the pathway will aid quantitative modeling and engineering of bacterial cells (e.g., for the production of medically relevant recombinant proteins).


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' end was considered to be an optimal position for 4.5S RNA labelling without compromising the functionality of 4.5S RNA in vivo for the following reasons: 1. The structure containing the most complete 4.5S RNA in complex with Ffh, FtsY, ribosome and translocon is shown in Fig. S1 1 . The resolved structure is missing the last 7 nucleotides at the 3' end due to the lower resolution in this region. However, as seen from the electron density map, the 3' end of 4.5S RNA does not form contacts with the other components and points away from all of the proteins and the ribosome. In other structures available from PDB 1,2 , the 3' end of 4.5S RNA is poorly resolved with a few tens of nucleotides in the 3' end missing from the structure. The lack of electron density itself suggest that this part of the molecule is flexible and not involved in stable interactions with other partners.

Supplementary Note 2. Statistical criteria to define number of diffusion states
To the best of our knowledge, there are no defined criteria for determination of exact number of diffusion states fully describing the mobility of biomolecules in vivo. Using simulated microscopy trajectories, representing molecules in discrete diffusion states in a confined cell volume, it has been shown that the commonly used algorithm vbSPT 5 overestimates the number of diffusion states, depending on the amount of data and complexity of the ground-truth model 6,7 . In addition, vbSPT cannot take into account dot localization uncertainties and motion blur, which is possible with our currently used algorithm. The Akaike information criterion (AIC), which is expected to predict the statistical quality of the model, also tend to overfit data 8 .
Even if there existed a perfect statistical criterion predicting the model size, we would still, however, expect significant difficulties in determination of the number of diffusion states in an ensemble of living cells. Whereas the simulated microscopy data used in the aforementioned analyses were generated assuming Brownian diffusion in cells of same shapes and sizes with homogeneous viscosity, live-cell analyses of diffusing particles most probably include some cell-to-cell and in-cell spatial heterogeneity in diffusion due to, e.g., different location and number of nucleoids in cells at different stages of the cell cycle. Furthermore, in relation to SRP tracking in the present analysis (and tRNA tracking in our previous analyses 8 ), we expect that the ribosome bound state would practically consist of a continuum of diffusion states, rather than a state described with defined diffusion coefficient, since elongating ribosomes can be bound alone on an mRNA or as polysomes with up to tens of ribosomes per mRNA. Hence, whereas the average diffusion coefficient is expected to be distinguishable between free 4.5S RNA, free SRP and ribosome bound SRP, the overall system is probably not described by a finite number of diffusion states, but rather by a number of diffusion ranges, more or less overlapping each other.    Figures 2, 4, S13 and S15.  Figure 2 (main text), but without mirroring across the long cell axis.

Supplementary Note 3. Estimation of fraction of membrane-associated molecules
We considered the steady-state total occupancy spatial distribution profile (T) of ribosome-bound state as a superposition of known "membrane" (M) and "cell interior" (C) profiles ( Fig. S10) with unknown weight α: = + (1 − ) . The membrane fraction α was obtained by least square fitting. Figure S10. Estimation of membrane fraction of total occupancy of the ribosome-bound state (state 1). Fitting of experimentally derived profile by the sum of two profiles: "membrane" (LacY data, Fig S8) and "cell interior" (theoretical prediction for evenly distributed particles in a cylindrical cell without end caps).
The same procedure was performed to estimate respective fractions of "membrane" component (M) in SRP-ribosome binding events profile (B) and SRP release events profile (R), i. e.: = + (1 − ) , = + (1 − ) . The membrane fractions β and were obtained by least square fitting.
As α, β and vary slightly depending on the size of the initial HMM model, the number of bins of the profile histograms, and also the size of margins used to cut cell poles and the middle part of the cell while projecting coordinates to the short cell axis, we varied these parameters and followed values of α, β and (Fig. S11). Mean values of α, β and are presented in Table S2, with errors obtained either as standard deviation from the least square fitting procedure, or as a standard deviation of scattered α, β and values obtained with different profile construction parameters, depending on which error was largest.
The same procedure was applied to determine the apparent membrane fraction in total occupancy of state 2 (free SRP) and state 3 (free RNA) and results are shown in Table S2.  Table S2. Mean values of membrane fractions α, β and derived from least square fitting of experimental profiles as a sum of "membrane" and "cell interior" profiles.

Supplementary Note 4. Linking derived SRP cycle model with earlier SRP-specific ribosome profiling data
The distribution of dwell times of SRP in ribosome-bound states, obtained from the ground truth of the simulated model (Fig. S21a, Table S3), was converted from time units to number of codons translated during the SRP dwell using a translation rate of 17 aa/s 15,16 (Fig. S19, blue bars). The histogram shows a gradually increasing profile, resulting from the diffusion-limited time for membrane search, and a long "tail" representing the exponentially distributed membrane bound time built in to the model.
The data from SRP-specific ribosome profiling experiment 17 (E. coli MC4100 strain grown in RDM at 37 °C) represents the transcriptome-wide SRP interactome aligned to the position of initial SRP binding (Fig. 2a in 17 ). Data from the published figure was digitalized using WebPlotDigitizer, background (mean translatome density) was subtracted, and the curve was normalized to the maximum value (Fig. S19, purple curve). The mean value of the SRP footprint from ribosome-profiling data was calculated to be 11 aa. Figure S19. Comparison of dwell times for SRP in ribosome-bound state obtained from our simulated model, with SRP footprints obtained from SRP-specific ribosomal profiling (transcriptome-wide SRP interactome aligned to the position of initial SRP binding) 17 . Figure S20. Schematic representation of a trajectory for particle experiencing transitions between state 2 → state 1 → state 2.  Table S3 and Table S4 respectively.